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Overton, Mays – Homework 28 – Due: Apr 13 2005, 4:00 am – Inst: Turner
1
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printout
should have
12
questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
The due time is Central
time.
001
(part 1 oF 2) 10 points
A moon oF a planet like the Earth is 579000 km
distant From the planet’s center, and it com
pletes an orbit in 35
.
4 days.
Determine the moon’s orbital speed.
Correct answer: 1189
.
44 m
/
s.
Explanation:
Using the obvious Formula
v T
= 2
π R ,
we obtain For the moon’s orbital speed
v
=
2
π R
T
=
2
π
(579000 km )
35
.
4 days
= 1189
.
44 m
/
s
.
002
(part 2 oF 2) 10 points
How Far does the moon ”Fall” toward the
planet in 1
.
29 s?
Correct answer: 2
.
03308 mm.
Explanation:
The centripetal acceleration
a
oF the motion
oF the moon is
a
=
v
2
R
=
(1189
.
44 m
/
s )
2
5
.
79
×
10
8
m
= 0
.
00244345 m
/
s
2
.
Hence, in time
t
the moon Falls a distance
d
=
1
2
a t
2
=
1
2
(0
.
00244345 m
/
s
2
) (1
.
29 s )
2
= 0
.
00203308 m
= 2
.
03308 mm
.
003
(part 1 oF 1) 10 points
A cylindrical habitat in space 7
.
35 km in di
ameter and 31
.
7 km long has been proposed
(by G.K. O’Neill, 1974). Such a habitat would
have cities, land, and lakes on the inside sur
Face and air and clouds in the center.
This
would all be held in place by rotation oF the
cylinder about its long axis.
The acceleration oF gravity is 9
.
8 m
/
s
2
.
How Fast would the cylinder have to rotate
to imitate the Earth’s gravitational feld at
the walls oF the cylinder?
Correct answer: 0
.
0516398 rad
/
s.
Explanation:
The radius oF a cylinder with
d
= 7
.
35 km
is
r
=
d
2
=
7
.
35 km
·
1000 m
1km
2
= 3675 m
.
To simulate the Earth’s gravitational feld
g
= 9
.
8 m
/
s
2
at the walls oF the cylinder the
Following relation must hold:
g
=
ω
2
r
=
v
2
r
.
ThereFore the angular speed
ω
oF the cylinder
has to be
ω
=
r
g
r
=
r
9
.
8 m
/
s
2
3675 m
= 0
.
0516398 rad
/
s
.
004
(part 1 oF 1) 10 points
Two satellites
A
and
B
orbit the same planet.
Both satellites have circular orbits oF respec
tive radia
r
A
and
r
B
= 2
r
A
.
The masses
oF the two satellites are respectively
m
A
and
m
B
= 3
m
A
.
A
B
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View Full Document Overton, Mays – Homework 28 – Due: Apr 13 2005, 4:00 am – Inst: Turner
2
What is the ratio of the orbital speeds of
the two satellites?
1.
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This note was uploaded on 03/22/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Turner
 Physics, Work

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